Electronic Structure of Metallophthalocyanines, MPc (M = Fe, Co, Ni, Cu, Zn, Mg) and Fluorinated MPc

We compute the electronic structure and optical excitation energies of metal-free and transition metal phthalocyanines (H2Pc and MPc for M = Fe, Co, Ni, Cu, Zn, Mg) using density functionaltheory with optimally-tuned range-separated hybrid functionals (OT-RSH).We show that the OT-RSH approach provides photoemission spectra in quantitative agreement with experimentsas well as optical band gaps within 10% of their experimental values, capturing the interplay of localized d-states and delocalized pi-pi* states for these organometallic compounds. We examine the tunability of MPcs and H2Pc through fluorination, resulting in quasi-rigid shifts of the molecular orbital energies by up to about 0.7 eV. Our comprehensive dataset provides a new computational benchmark for phthalocyanines molecules, significantly improving upon other density-functional-theory-based approaches. We compute the electronic structure and optical excitation energies of metal-free and transition-metal phthalocyanines (H 2 Pc and MPc for M = Fe, Co, Ni, Cu, Zn, Mg) using density functional theory with optimally-tuned range-separated hybrid functionals (OT-RSH). We show that the OT-RSH approach provides photoemission spectra in quantitative agreement with experiments as well as optical band gaps within 10% of their experimental values, capturing the interplay of localized d-states and delocalized π − π ∗ states for these organometallic compounds. We examine the tunability of MPcs and H 2 Pc through ﬂuorination, resulting in quasi-rigid shifts of the molecular orbital energies by up to (cid:39) 0.7 eV. Our comprehensive dataset provides a new computational benchmark for gas-phase phthalocyanines, signiﬁcantly improving upon other density-functional-theory-based approaches.

theory (DFT) has been the dominant computational approach for understanding the degree of localization of the molecular orbitals of MPcs, yet has shown high variability depending on the choice of the exchange and correlation functionals 7,[21][22][23][24][25][26] , with different levels of approximation leading to distinct energy ordering of the molecular levels. Moreover, standard DFT functionals, such as the local density approximation (LDA), generalized gradient approximations (GGAs), and hybrid functionals like B3LYP, PBEh and HSE, often lead to poor agreement with photoemission experiments. In contrast, quantitative agreement was obtained for H 2 Pc 27,28 , CuPc 29,30 , CoPc 31 , and ZnPc 32 using approaches that incorporate the correct asymptotic behavior of the exchange-correlation potential, such as range-separated hybrid functionals 33 and the GW method 34 . While promising, and to the best of our knowledge, these approaches have yet to be applied to, and benchmarked against, a broad range of metal phthalocyanines. In this work, we compute the electronic structure of gas-phase phthalocyanines for an extensive set of molecules, including H 2 Pc, MgPc, as well as 3d transition metals Fe, Co, Ni, Cu, Zn from 3d 6 to 3d 10 and their fluorinated counterparts H 2 PcF 16 , CoPcF 16 and ZnPcF 16 , by using the OT-RSH method. We show that the OT-RSH approach provides quantitative agreement with experiment for both molecular orbital energies and optical bandgaps for all of these compounds, with the level ordering qualitatively differing from conventional DFT approaches 24 . We show that fluorination in these compounds can be used to induce significant energy shifts of the molecular levels, due to the significant change in the molecular quadrupole upon fluorination. Our results underline the potential of the OT-RSH approach for understanding the properties of known organo-metallic compounds and predicting the properties of unknown ones.
The OT-RSH approach is a generalized Kohn-Sham scheme 35 , in which the non-local exchange potential explicitly depends on the Kohn-Sham orbitals through the Fock operator. In the RSH scheme 36,37 , the Coulomb operator is divided into short-range (SR) and long-range (LR) components by a rangeseparation parameter γ. Noteworthily, by construction, the LR component in the OT-RSH formalism has the asymptotically correct (α + β )/r behavior (with α + β = 1 in the gas-phase) 33 , with the remaining choices in the construction of the functional being the fraction of Fock exchange applied in the SR component (α), and the range separation parameter γ. While α can generally be chosen to match values of other global hybrid functionals, the values of γ tend to be highly system-dependent.
γ defines the length-scale where the short-range is transitioned into long-range interactions, and is included in both the short-range and long-range exchange expressions 33 , therefore a key parameter in determining the quantitative accuracy of the final results. A parameter-free approach for finding the system-specific γ value has been proposed by Stein, Kronik and Baer 27,30,[38][39][40] , with γ chosen to maximize the compliance with the Koopman's theorem. Namely, the optimal γ opt is obtained by minimizing: where IE and EA are the ionization energy and electron affinity of the molecule, and ε γ HOMO and ε anion,γ HOMO are the highest occupied molecular orbital (HOMO) of neutral and negatively charged system.
Minimizing only J 2 IE is also commonly used as the optimal γ of J 2 IE and J 2 have been empirically found to be in close agreement 27,31 .
We perform DFT and time-dependent DFT (TDDFT) calculations using the QChem 41 48 ; CuPc from gas-phase electron diffraction (GED) 49 ; NiPc from GED 50 ; ZnPc from XRD 51 , GED 52 ; MgPc from XRD 53 , GED 52 ; H 2 Pc from XRD and neutron-diffraction 54 The molecular geometries are all optimized using the B3LYP functional 55 , providing structural parameters in agreement with experiments, as shown in Table 1. The geometry of MPc is shown in  Table S1 for all Pcs studied in this work. Results discussed in the following are for values of α=0.1, following a previous study with OT-RSH for CoPc 31 , while results for α = 0.2 are included in the Supporting Information (SI) for comparison. We find that the HOMO/LUMO levels are weakly dependent on the choice of α as shown in Table S1 with a difference in energy smaller than 0.05 eV for both HOMO and LUMO.
Results on the electronic structure obtained from OT-RSH for all MPcs in this work are summarized in Fig. 2, with results from α of 0.2, B3LYP and CAMB3LYP 56 included in Figs. S3-S5 for comparison. In agreement with experiment, we find that bandgap, ionization energy, and electronic affinity are weakly dependent on the nature of the central atom, varying by less than 0.1eV for 6 of the 7 molecules, with the exception of FePc for which the higher spin configuration leads to a ∼ 0.2eV reduction of the HOMO-LUMO gap. HOMO energies from OT-RSH are within 0.3eV of experimental ionization potentials 17 , and agree well with GW calculations 29 for CuPc with HOMO of 6.27 eV. Those results are much improved over B3LYP (Fig. S4), HSE 8 and CAMB3LYP (Fig. S5), as shown in Table 2.
For all MPcs studied in this work, the HOMO is of a 1u symmetry with no d-character, and LUMO is of e g symmetry and with (d xz , d yz )-character for the transition metals. This result is in agreement with HSE 8 and B3LYP results from previous study 21,22 and the current work (see Fig. S4), while disagreeing with a previous study reporting contribution of e g (d xz,yz ) to FePc HOMO from Vosko-Wilk-Nusair (VWN) 24 ; b 1g (d x 2 −y 2 ) to NiPc, CuPc LUMO from VWN 24 and PBE 21,22 ; a 1g (d z 2 ) to FePc HOMO and b 1g (d x 2 −y 2 ) to CuPc LUMO from DFT+U 7 . We find that the mixing of the d-orbitals with the organic ligand states strongly depends on their magnetic quantum number and their empty/occupied character, as shown in Fig. 2.
FePc CoPc NiPc CuPc ZnPc MgPc H 2 Pc  As shown in Fig. 2, the LUMOs of all MPcs are doubly degenerate of e g symmetry, which allows the mixing of d xz , d yz states having out-of-plane character. From Fe (3d 6 ) to Zn (3d 10 ), the fraction of (d xz,yz ) decreases from 6.5% to 0.3%, as shown in  Interestingly, despite the significant change in orbital energy due to fluorination, qualitative symmetry and composition features are maintained for the molecular orbitals, as shown in Fig. 2 and Table 2. This may allow for additional tunability of photocatalytic reactivity, and band alignment in MPc-containing heterojunctions, which are critical in controling the rate of charge transfer that governs the performance of such heterojunctions 60-62 . MPcs vary only slightly, and are almost all from HOMO to LUMO, as shown in Table 3. For those involving other molecular orbitals, the excitations are also from occupied states with no d fraction to LUMO. Therefore the excitations are mainly from ligand to LUMO states which include small fraction of d-orbitals.

Conflicts of interest
There are no conflicts to declare.

Notes and references
download file view on ChemRxiv MPc_ElectrStr.pdf (7.55 MiB)   The optimal γ opt values vary slightly for MPcs with different transition metals. γ opt can also be slightly affected by the basis set, which can be the reason for slightly different γ opt values obtained here from previous studies, i.e. for    (Fig. 2). Meanwhile, the HOMO and HOMO-1 energy differences are much larger from CAMB3LYP than that from OT-RSH.      Fig. S8 (a) and (b). The dashed horizontal lines indicates approximate averaged electrostatic potential in the middle of the molecules. The change of electrostatic potential ∆V is around 0.7∼0.8 eV, which is consistent with the orbital energy level shifts.